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Two-mass two spring system

  1. Oct 29, 2008 #1
    1. The problem statement, all variables and given/known data

    I have a two spring 2 mass system, with masses m1 and m2, spring constants k1 and k2. There is also an external harmonic force acting on m2, [tex]F sin(\omega\ t )[/tex]

    I have to obtain the free ocsillation frequencies [tex]\omega_{1}[/tex] and [tex]\omega_{2}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    i obtained the following eqns by applying newtons 2nd law to each of the masses

    [tex]m_{1}x_{1}'' = -k_{1}x_{1}+k_{2}(x_{2}-x_{1})[/tex]

    [tex]m_{2}x_{2}'' = -k_{2}(x_{2}-x_{1})+F sin(\omega\ t)[/tex]

    and this is where i am stuck, the notes I have suck tbh and i have no idea what to do next, would be very greatfull for some help.
  2. jcsd
  3. Oct 29, 2008 #2


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    Welcome to PF!

    uiop qwertybob! Welcome to PF! :smile:

    I don't get it …

    where are the masses and the springs in relation to each other? :confused:
  4. Oct 29, 2008 #3
    sorry i guess i should have mentioned that, hopefully this makes it clear


    k1 connects m1 to a fixed point, k2 connects m1 and m2. displacement of m1 = x1, displacement of m2 = x2.

    ty for the kind welcome :smile:
  5. Oct 30, 2008 #4


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    uiop qwertybob! :smile:

    (have an omega: ω :wink:)
    ah! … a fixed point! … all is clear! :biggrin:

    ok … multiply each equation by a constant, and add, so that takes the form (ax1 + bx2)'' = c(ax1 + bx2) + Gsinωt.
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